This applet can be used to explore calculating probabilities for independent events.[br][br]e.g. using the default dimensions.[br][br]Check the left hand tick box, move the fish into the red zone A. What is the probability of the fish being in area A, P(A)?[br][br]By considering the depth [math]P\left(A\right)=\frac{2}{7}[/math][br][br]Unchecked the left-hand box and check the top one. What is the probability of the fish being in area B, P(B)?[br][br]By considering the width of the tank [math]P\left(B\right)=\frac{3}{8}[/math][br][br]Now check the left hand box again. What is the probability of the fish being in region A and B at the same time? This time we need to think about the area.[br][br][math]P\left(A\cap B\right)=\frac{2\times3}{7\times8}=\frac{6}{56}=\frac{3}{28}[/math][br][br]But it should also be evident that this equivalent to multiplying the fractions. i.e. we want [math]\frac{2}{7}\text{ of }\frac{3}{8}[/math] .[br][br]This can be followed by a discussion of assumptions, i.e. the events must be independent.[br][br]Further problems can be generated by moving the cross-hairs to re-dimension the tank and regions.[br][br]There is a worksheet attached that allows students to explore multiplication of probabilities for 'and' probability problems.